The Odds of Staying on Budget

Christoph Haase; Stefan Kiefer

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arXiv · 1409.8228

The Odds of Staying on Budget

Christoph Haase·Stefan Kiefer

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Abstract

Given Markov chains and Markov decision processes (MDPs) whose transitions are labelled with non-negative integer costs, we study the computational complexity of deciding whether the probability of paths whose accumulated cost satisfies a Boolean combination of inequalities exceeds a given threshold. For acyclic Markov chains, we show that this problem is PP-complete, whereas it is hard for the PosSLP problem and in PSPACE for general Markov chains. Moreover, for acyclic and general MDPs, we prove PSPACE- and EXP-completeness, respectively. Our results have direct implications on the complexity of computing reward quantiles in succinctly represented stochastic systems.

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Christoph Haase, Stefan Kiefer. 2014-09-21. The Odds of Staying on Budget. https://arxiv.org/abs/1409.8228

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